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Measurement Techniques. DC Circuits Feb. 2009. Measurement Techniques DC Circuits . Resistance (R) Ohms, Ω , K Ω , M Ω Voltage (V) Volt, AC, DC, mV, KV Current (I) Amp, mA (milliamps), uA (microamps). Series Circuit RT = R1 + R2 + R3. R T Ω. R T. R1 R2 R3.

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measurement techniques

Measurement Techniques

DC Circuits

Feb. 2009

measurement techniques dc circuits
Measurement Techniques DC Circuits
  • Resistance (R)
    • Ohms, Ω, KΩ, MΩ
  • Voltage (V)
    • Volt, AC, DC, mV, KV
  • Current (I)
    • Amp, mA (milliamps), uA (microamps)
bread board techniques series circuits resistance measurement

Series Circuit

RT = R1 + R2 + R3

RTΩ

RT

R1

R2

R3

Bread Board Techniques - Series Circuits Resistance Measurement
  • Measurement must be made without power applied or wired to the circuit.
  • Individual components must be removed from the circuit to measure the value accurately.

Given R1= 100, R2= 4.7K, R3=100K Find RT

breadboard techniques series circuit voltage measurement

Vs

12V

VR1

R1

R2

R3

Vs

VR2

VR3

Vs = VR1 + VR2 + VR3

Breadboard Techniques - Series Circuit Voltage Measurement
  • The voltage supplied by the (12V) voltage source is proportionally distributed across each resistor.
  • The higher the resistor value, the greater the voltage drop
  • Kirchoffs Law – The sum of the voltage drop across each resistor in the circuit will add up to the source voltage
calculating voltage drops

Vs

12V

IT

VR1

R1

R2

R3

Vs

VR2

VR3

VR1 = IT x R1

VR2 = IT x R2

VR3 = IT x R3

Calculating Voltage Drops

RT = R1 + R2 + R3

  • Determine total resistance RT
  • Using Ohms Law calculate total current IT
  • Using Ohms Law again, calculate the voltage drop across R1, R2, R3

IT = Vs / RT

bread board techniques series circuit current measurement

IR1

IT

R1

R2

R3

Vs

Vs

12V

IR2

IT

IT

IT

IR3

IT = IR1 = IR2 = IR3

IT

Bread Board Techniques - Series Circuit Current Measurement
  • The meter must be configured for current measurement.
  • The circuit must be “opened” and the meter placed (anywhere) in series.
  • The same current flows from the voltage source, “through” the meter, each resistor, and then back to the source.
bread board techniques parallel circuits resistance

RTΩ

RT

R1 R2 R3

Bread Board Techniques – Parallel CircuitsResistance
  • Circuit must be removed from the voltage source
  • The total resistance is “less than” the smallest resistor value
  • Avoid finger contact when measuring

1

parallel circuits calculating total resistance

1 1 1 1

RTΩ

Parallel Circuit

RT R1 + R2 + R3

=

RT

R1 R2 R3

Parallel CircuitsCalculating Total Resistance

R1//R2//R3 Where R1 is in parallel with R2 which is in parallel with R3

product over sum method

Let Rp = R1 // R2

R1 x R2

R1 + R2

Rp =

R1 R2 R3

Now RT = Rp // R3

RT

Rp x R3

Rp + R3

RT =

Product-Over-Sum Method
  • Calculate the parallel resistance of any 2 resistors at a time.
  • First do R1//R2 using the Product-Over-Sum method
  • Then use the R1/2 resistance in parallel with R3
parallel circuits voltage measurement

R1 R2 R3

Parallel Circuits Voltage Measurement

The source voltage (Vs) is common to all components in the circuit

Vs = VR1 = VR2 = VR3

Vs

parallel circuits current measurement

I1

I2

I3

IT

Parallel Circuits Current Measurement

I1 + I2 + I3

Vs

R1

R2

R3

I2 + I3

IT= I1 + I2+ I3

parallel circuits current calculations

IT

I1

I2

I3

Vs

R1

R 2

R3

Parallel CircuitsCurrent Calculations

To measure current the circuit must be broken and the current meter must be placed in series with the component.

calculating total current i t

Vs

50V

R1

150 Ω

R2

300 Ω

R3

100 Ω

Calculating Total Current (IT)
  • First find total resistance RT

2. Then use Ohm’s Law to find total current

Using Product-Over-Sum Method

R1//R2 = (150 x 300) / (150 + 300) = 100 ohms

Rp//R3 = (100 x 100) / (100 + 100) = 50 ohms

Note: when the parallel resistors are equal in value, just divide by the number of R’s

3K//3K = 1.5K

6K//6K//6K = 2K

Using Reciprocal Method

1/RT = 1/R1 + 1/R2 + 1/R3 = 1/150 + 1/300 + 1/100

= 0.00666 + 0.00333 + 0.01 = 0.020

RT = 1/ 0.020 = 50 ohms

calculating total current i t14

Vs

50V

R1

150 Ω

R2

300 Ω

R3

100 Ω

Total Current IT

Vs

RT

IT =

Calculating Total Current (IT)
  • First find total resistance RT

2. Then use Ohm’s Law to find total current

50 v

= -------- = 1 amp

50 Ω

The power supply must be capable of supplying at least 1 amp of current

calculating branch currents
Calculating Branch Currents

RT = 50 ohms IT = 1 amp

IT

I1

I2

I3

Vs

50 V

R1=150

R2=300

R3=100

I1 = Vs / R1 = 50/150 = 0.333333 amps

I2 = Vs / R2 = 50/300 = 0.166666 amps

I3 = Vs / R3 = 50/100 = 0.200000 amps

1.00 amp

series parallel circuits
Series/Parallel Circuits
  • There are multiple current paths.
  • Resistors may be in series or parallel with other resistors.
  • A node is where three or more paths come together.
  • The total power is the sum of the resistors’ power.
simple combo circuit

--/\/\/\/\--

Rs

I

R

E

Simple Combo circuit

Reduce the parallel connection to its series equivalent

R2 // R3 = Rs

Then reduce the series equivalent to the total resistance as seen by the source

RT = R1 + Rs

reduce simplify

R1 R3

R2 R4

R1 R3

+ +

R2 R4

RT = R1,2 // R3,4

Reduce & Simplify
analysis of a combo circuit

100 200

200 400

12 V

Analysis of a combo circuit
  • Calculate
  • Total current
  • Branch currents
  • IR drops

Board Solution

reduce simplify find r t

100 200

200 400

300 600

12 V

12 V 200 Ώ

Reduce & Simplify – find RT

RT = R1,2 // R3,4

= 300 // 600 = 200

IT = 12 / 200 = 0.06 amps (60 mA)

determining total resistance

R1 R2 R3

R1 R2 R3

RT

IT

Determining Total Resistance

1 1 1 1

RT = R1 + R2 + R3

V

RT

RT = V

IT

branch currents

100 200

200 400

300 600

12 V

Branch Currents

IT Ia Ib

Branch Currents

Ia = 12 / 300 = 40 mA

Ib = 12 / 600 = 20 mA

IT = Ia + Ib = 40mA + 20 mA = 60 mA

ir drops voltage across each resistor

60 mA 40 mA 20 mA

R1 R3

100 200

R2 R4

200 400

12 V

IR Drops (voltage across each resistor)

VR1 = 40 mA x 100 = 4000 mV = 4V

VR2 = 40 mA x 200 = 8000 mV = 8V

VR3 = 20 mA x 200 = 4000 mV = 4V

VR4 = 20 mA x 400 = 8000 mV = 8V

bridge circuit

VA = R2 x Vs

R2 + R1

VB = R4 x Vs

R4 + R3

R1 R3

R2 R4

AB

Vs

VAB

VA

VB

Bridge Circuit

In a bridge circuit the voltage difference between the two parallel branches is used to indicate the potential difference between the two points.

VAB = VA - VB

Using the Voltage Divider Formula

wheatstone bridge null balance detector
Wheatstone Bridge – null balance detector

VOUT = 0 volts

A balanced bridge can be used to measure an unknown resistance.

The Wheatstone bridge can be used as an “ohmmeter” by comparing the unknown resistance value to a known one.

conditioning circuit for resistive sensors and transducers

R1

R1

VOUT

A

B

Vs

R1

Rs

Conditioning circuit for resistive sensors and transducers
  • VOUT can be used to represent some type of process variable
  • Temperature
    • Thermistor
    • Resistance Temperature Detectors (RTD’s)
  • Pressure
    • Strain Gauge
  • Flow
    • Anemometer

The bridge is often used as a conditioning circuit to convert the output of aresistivetype sensing element into a voltage (mV)